Linda J S Allen

..These relations are illustrated, analytically and numerically, in two settings, a general stage-structured model and a vector-host model applied to West Nile virus in mosquitoes and birds...

..For population sizes N=/>1000, the deterministic and stochastic models agree, but for small population sizes the stochastic models indicate that the backward bifurcation may have little effect on the disease dynamics...

..Environmental changes that result in greater habitat overlap result in more encounters among various species that may lead to pathogen outbreaks and pathogen establishment in a new host...

..These new models capture some of the realistic dynamics of the male/female rodent hantavirus interaction: higher seroprevalence in males and variability in seroprevalence levels...

..Finally, numerical simulations are conducted to explore the effect of disease on two-species competition, to illustrate some of the analytical results and to highlight some of the differences in the stochastic and deterministic models...

..Numerical examples illustrate the dynamics of the two- and three-host epidemic models. The models have applications to hantavirus in rodents and other zoonotic diseases with multiple hosts...

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..The original model of Leonard has this same property. However, with random selection values, solutions tend to converge toward the polymorphic equilibrium...

..It is shown that the probability of a successful invasion depends on the initial viral dose, whether the immune system is activated, and whether the release strategy is bursting or budding...

..Given an outbreak occurs, the total number of cases for the CTMC model is in good agreement with the ODE model. The greatest number of drug resistant cases occurs if treatment is delayed or if only symptomatic individuals are treated...

..Numerical examples illustrate the dynamics of the models. The biological implications of the results and future research goals are discussed in the conclusion...

..If ℛ(0)>1 and ℛ(F)<1, then the population becomes disease-free. However, if both thresholds are greater than one, the population levels are severely reduced by the fungal pathogen...

..In this investigation, we summarize some of the deterministic and stochastic threshold theory, illustrate how to calculate the stochastic thresholds, and derive some new relationships between the deterministic and stochastic thresholds...

..The results are shown to hold in epidemic models with periodic demographics that include temporary immunity, isolation, and multiple strains...

..Computational results demonstrate how dramatically the mean persistence time can vary for different populations that experience the same logistic growth...

..It is shown through analysis and numerical simulations that both diseases can be maintained within a single host population, where individuals can be either infected with both viruses or with a single virus...

..The initial number of infected individuals, the basic reproduction numbers, and other epidemiological parameters are important determinants of the dominant strain in the stochastic epidemic model...

..Furthermore, if migration rates are low, one or more than one patch may be successfully invaded, while if migration rates are high all patches are invaded...

..In addition, an example is given which shows that if such inequalities are not satisfied then coexistence may occur...

..We also derive a stochastic differential equations (SDE) model of the Itô type based on our deterministic model. Our simulations reveal good agreement between the deterministic model and the SDE model...